System of Particles and Rotational Motion

An infinite number of charges, each equal to q, are placed along the x-axis at x=1, x=2, x = 4, x=8 and so on. What is the potential at x = 0 due to this set of charges ?

An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 ms^-1 and the second part of mass 2 kg moves with 8 ms^-1 speed. If the third part flies off with 4 ms^-1 speed, then its mass is

• 3 kg

• 5 kg

• 7 kg

• 17 kg

A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in figure. When string is cut, the initial angular acceleration of the rod is

• $\frac{3\mathrm{g}}{2\mathrm{L}}$

• $\frac{\mathrm{g}}{\mathrm{L}}$

• $\frac{2\mathrm{g}}{\mathrm{L}}$

• $\frac{2\mathrm{g}}{3\mathrm{L}}$

A solid uniform sphere resting on a rough horizontal plane is given a horizontal impulse directed through its centre so that it starts sliding with an initial velocity v₀. When it finally starts rolling without slipping the speed of its centre is

• $\frac{2}{7} {\mathrm{v}}_0$

• $\frac{3}{7} {\mathrm{v}}_0$

• $\frac{5}{7} {\mathrm{v}}_0$

• $\frac{6}{7} {\mathrm{v}}_0$

Three identical square plates rotate about the axes shown in the figure in such a way that their kinetic energies are equal. Each of the rotation axes passes through the centre of the square. Then the ratio of angular speeds ω₁ : ω₂ : ω₃ is

• 1 : 1 : 1

• $\sqrt{2} : \sqrt{2} : 1$

• $1 : \sqrt{2} : 1$

• $1 : 2 : \sqrt{2}$

A large number of particles are placed around the origin, each at a distance R from the origin. The distance of the centre of mass of the system from the origin is

• equal to R

• less than equal to R

• greater than R

• greater than equal to R

Two particles A and B are moving as shown in the figure.

Their total angular momentum about the point O is

• 9.8 kg m² / s

• zero

• 52.7 kg m² / s

• 37.9 kg m² / s

A circular disc rolls on a horizontal floor without slipping and the centre of the disc moves with a uniform velocity v. Which of the following values of the velocity at a point on the rim of the disc can have ? 

• v

• − v

• 2v

• Zero